Novel techniques to analyze dynamical properties of quantum chaos with peculiar evidence of hybrid systems confinement.

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Computation and convergence of fixed-point with an RLC-electric circuit model in an extended b-suprametric space.

This article establishes various fixed-point results and introduces the idea of an extended b-suprametric space. We also give several applications pertaining to the existence and uniqueness of the solution to the equations concerning RLC electric circuits. At the end of the article, a few open questions are posed concerning the distortion of Chua's circuit and the formulation of the Lagrangian for Chua's circuit.

Fractional epidemic model of coronavirus disease with vaccination and crowding effects.

Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh-Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

A comparative analysis of three distinct fractional derivatives for a second grade fluid with heat generation and chemical reaction.

This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE's is transformed into ODE's by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects.

Enhancing automic and optimal control systems through graphical structures.

The concept of graphical structures of extended suprametric space is introduced in this study and applied to supra-graphical contractive mapping. A recursive algorithm in connection with graphical notions can be employed in adaptive systems to construct a desired output function iteratively after specific conditions are first defined to ensure the existence of the solution by use of supra-graphical contractive mapping. After analyzing the historical context and relevant outcomes, we discuss the usage of graphical structures and supra-graphical contractive mappings in the conceptual frameworks of adaptive control and optimal control systems.

Machine learning intelligent based hydromagnetic thermal transport under Soret and Dufour effects in convergent/divergent channels: a hybrid evolutionary numerical algorithm.

In this research, we analyze the complex dynamics of hydro-magnetic flow and heat transport under Sorent and Dofour effects within wedge-shaped converging and diverging channels emphasizing its critical role in conventional system design, high-performance thermal equipment. We utilized artificial neural networks (ANNs) to investigation the dynamics of the problem. Our study centers on unraveling the intricacies of energy transport and entropy production arising from the pressure-driven flow of a non-Newtonian fluid within both convergent and divergent channel. The weights of ANN based fitness function ranging from - 10 to 10. To optimize the weights and biases of artificial neural networks (ANNs), employ a hybridization of advanced evolutionary optimization algorithms, specifically the artificial bee colony (ABC) optimization integrated with neural network algorithms (NNA). This approach allows us to identify and fine-tune the optimal weights within the neural network, enabling accurate prediction. We compare our results against the established different analytical and numerical methods to assess the effectiveness of our approach. The methodology undergoes a rigorous evaluation, encompassing multiple independent runs to ensure the robustness and reliability of our findings. Additionally, we conduct a comprehensive analysis that includes metrics such as mean squared error, minimum values, maximum values, average values, and standard deviation over these multiple independent runs. The minimum fitness function value is 1.32 × 10-8 computed across these multiple runs. The absolute error, between the HAM and machine learning approach addressed ranging from 3.55 × 10-7 to 1.90 × 10-8. This multifaceted evaluation ensures a thorough understanding of the performance and variability of our proposed approach, ultimately contributing to our understanding of entropy management in non-uniform channel flows, with valuable implications for diverse engineering applications.

Heat generation/absorption effect on natural convective heat transfer in a wavy triangular cavity filled with nanofluid.

This study is numerically executed to investigate the influence of heat generation or absorption on free convective flow and temperature transport within a wavy triangular enclosure filled by the nanofluid taking the Brownian effect of nanoparticles. The water (H2O) is employed as base fluid and copper (Cu) as nanoparticles for making effective Cu-H2O nanofluids. The perpendicular sinusoidally wavy wall is cooled at low temperature while the horizontal bottom sidewall is heated non-uniformly (sinusoidal). The inclined wall of the enclosure is insulated. The governing dimensionless non-linear PDEs are executed numerically with the help of the Galerkin weighted residual type finite element technique. The numerically simulated results are displayed through average Nusselt number, isothermal contours, and streamlines for the various model parameters such as Hartmann number, Rayleigh number, heat generation or absorption parameter, nanoparticles volume fraction, and undulation parameter. The outcomes illustrate that the temperature transport rate augments significantly for the enhancement of Rayleigh number as well as nanoparticles volume fraction whereas reduces for the increment of Hartman number. The heat transfer is significantly influenced by the size, shape, and Brownian motion of the nanoparticles. The rate of heat transport increases by 20.43% considering the Brownian effect for 1% nanoparticle volume. The thermal performance increases by 8.66% for the blade shape instead of the spherical shape of nanoparticles. In addition, heat transfer is impacted by the small size of nanoparticles. The thermal transport rate increases by 35.87% when the size of the nanoparticles reduces from 100 to 10 nm. Moreover, the rate of heat transmission increases efficiently as the undulation parameter rises. It is also seen that a crucial factor in the flow of nanofluids and heat transmission is the heat generation/absorption parameter that influences temperature distribution, heat transfer rates, and overall thermal performance.